No solutions found

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x8"   was replaced by   "x^8". 

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     22*x-17-(12*x^8)=0 

Step  1  :

Equation at the end of step  1  :

  (22x - 17) -  (22•3x8)  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -12x⁸ + 22x - 17  =   -1 • (12x⁸ - 22x + 17) 

Polynomial Roots Calculator :

 3.2    Find roots (zeroes) of :       F(x) = 12x⁸ - 22x + 17
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  12  and the Trailing Constant is  17.

 The factor(s) are:

of the Leading Coefficient :  1,2 ,3 ,4 ,6 ,12
 of the Trailing Constant :  1 ,17

 Let us test ....

Note - For tidiness, printing of 19 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Equation at the end of step  3  :

  -12x8 + 22x - 17  = 0 

Step  4  :

Equations of order 5 or higher :

 4.1     Solve   -12x⁸+22x-17 = 0

Handling of functions of an even degree greater than 6 is not implemented yet

No solutions found